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- Ken Ono
- 2008

and he conjectured further such congruences modulo arbitrary powers of 5, 7, and 11. Although the work of A. O. L. Atkin and G. N. Watson settled these conjectures many years ago, the congruences… (More)

- Kathrin Bringmann, Ken Ono
- 2005

In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for Ne(n) (resp. No(n)), the number of partitions of n with even… (More)

S. Chowla conjectured that for a given prime p there are infinitely many imaginary quadratic fields whose class number is not a multiple of p. For p = 2 this conjecture is a consequence of Gauss’s… (More)

- Ken Ono
- 2008

Together with his collaborators, most notably Kathrin Bringmann and Jan Bruinier, the author has been researching harmonic Maass forms. These non-holomorphic modular forms play central roles in many… (More)

- Scott Ahlgren, Ken Ono
- 2004

If p is prime, then let φp denote the Legendre symbol modulo p and let p be the trivial character modulo p. As usual, let n+1Fn(x)p := n+1Fn „ φp, φp, . . . , φp p, . . . , p | x « p be the Gaussian… (More)

- Scott Ahlgren, Ken Ono
- Proceedings of the National Academy of Sciences…
- 2001

Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were… (More)

- Ken Ono
- 1995

Let p(n) denote the number of partitions of a non-negative integer n. A well-known conjecture asserts that every arithmetic progression contains infinitely many integers M for which p(M) is odd, as… (More)

- George E. Andrews, Jorge Jiménez-Urroz, Ken Ono
- 2001

As usual, define Dedekind’s eta-function η(z) by the infinite product η(z) := q1/24 ∞ ∏ n=1 ( 1 − qn) (q := e2πiz throughout). In a recent paper, D. Zagier proved that (note: empty products equal 1… (More)

- Ken Ono
- 2006

Let j(z) be the usual modular function for SL2(Z) j(z) = q−1 + 744 + 196884q + 21493760q + · · · , where q = e . The values of modular functions such as j(z) at imaginary quadratic arguments in H,… (More)

- Scott Ahlgren, Ken Ono
- 2005

We investigate divisibility properties of the traces and Hecke traces of singular moduli. In particular we prove that, if p is prime, these traces satisfy many congruences modulo powers of p which… (More)